The state you are thinking of is Alaska. It borders Canada and the Pacific Ocean, but not any of the other 49 States.
Idaho
Counting subsea boundaries (continental shelf) Canada borders:United States of AmericaNorwayDenmarkRussiaFrance (Saint Pierre and Miquelon )
Canada borders the Arctic Ocean to the north. On the other side of the Arctic Ocean is Russia.
Canada borders New York.
Montana does, but many other states have longer borders with Canada
The US shares borders with two other states (countries) - Canada and Mexico
Canada has only two land borders with the US. One with the contiguous states and the other with Alaska. These are therefore the two shortest and longest borders.
I guess you mean if both countries do share borders with other nations. In that case, they do: the US also borders Canada and Mexico also borders Guatemala and Belize.
No more or less famous than any other country.
Canada. The US only borders two other countries, Mexico to the south and Canada to the North.
No other state borders Alaska. Alaska is surrounded by water and Canada. The Canadian province of British Columbia and Canada's Yukon Territory border Alaska to the east. Alaska has a maritime border with Russia to the west across the Bering Strait. To the north is the southern part of the Arctic Ocean. The Pacific Ocean lies to the south and southwest.